Forest Ecology and Management 260 (2010) 313–320
Contents lists available at ScienceDirect
Forest Ecology and Management
journal homepage: www.elsevier.com/locate/foreco
Accuracy and suitability of selected sampling methods within conifer
dominated riparian zones
Theresa Marquardt a,1 , Hailemariam Temesgen b,∗ , Paul D. Anderson c,2
a
b
c
Department of Forest Engineering, Resources and Management, Oregon State University, 237 Peavy Hall, Corvallis, OR 97331–5703, USA
Department of Forest Engineering, Resources and Management, Oregon State University, 280 Peavy Hall, USA
Land and Watershed Management Program, USDA Forest Service, Pacific Northwest Research Station, 3200 SW Jefferson Way, Corvallis, OR 97331, USA
a r t i c l e
i n f o
Article history:
Received 19 December 2009
Received in revised form 13 April 2010
Accepted 13 April 2010
Keywords:
Pacific Northwest
Stand structure
Sampling
Monitoring
Douglas-fir
a b s t r a c t
Sixteen sampling alternatives were examined for their performance to quantify selected attributes of
overstory conifers in riparian areas of western Oregon. Each alternative was examined at eight headwater forest locations based on a 0.52 ha square stem maps. The alternatives were evaluated for selected
stand attributes (trees per hectare, basal area per hectare and height to diameter ratio), using root mean
square error, absolute percent bias, and mean absolute deviation as criteria. In general, rectangular strip
designs outperformed fixed area circular or radial plots and variable area plots. Sampling 3.6 m wide
strips perpendicular to the stream outperformed all other alternatives.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
This study examines the accuracy and suitability of a variety
of sampling methods to quantify stand attributes of conifer dominated riparian forests of western Oregon. Forest structure can
be described in a variety of ways such as species composition
(Aguirre et al., 2003; Nierenberg and Hibbs, 2000; Harper and
Macdonald, 2001; Coroi et al., 2004; Pabst and Spies, 1999) or measures of tree density (Coroi et al., 2004; Lhotka and Loewenstein,
2006), basal area per hectare (Pabst and Spies, 1999), diameter distribution (Chen and Bradshaw, 1999; Mason et al., 2007),
height distribution (Chen and Bradshaw, 1999), crown diameter
(Chen and Bradshaw, 1999), canopy characteristics (Nierenberg
and Hibbs, 2000; Harper and Macdonald, 2001; Pabst and Spies,
1999; Lhotka and Loewenstein, 2006), snag density (Harper and
Macdonald, 2001; Pabst and Spies, 1999), or downed wood (Harper
and Macdonald, 2001). The best sampling alternative is that which
most accurately quantifies the attributes of interest in typically
diverse riparian forests.
∗ Corresponding author. Tel.: +1 541 737 8549; fax: +1 541 737 3039.
E-mail addresses: Theresa.Marquardt@oregonstate.edu (T. Marquardt),
hailemariam.temesgen@oregonstate.edu (H. Temesgen), pdanderson@fs.fed.us
(P.D. Anderson).
1
Tel.: +1 541 737 8549; fax: +1 541 737 3039.
2
Tel.: +1 541 758 7786; fax: +1 541 750 7329.
0378-1127/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.foreco.2010.04.014
Quantifying stand attributes within riparian areas can be
extremely difficult. Riparian areas rank among the most complex,
variable and dynamic terrestrial habitats in the world (Coroi et
al., 2004). This is no different in the Pacific Northwest (Acker et
al., 2003). Horizontal and vertical structure are all highly variable within riparian areas of headwater streams (Richardson and
Danehy, 2007). For example, stand-level variations in density,
diameter and total tree height occur for both conifer and hardwood components. Snags within riparian areas add to the variety
of vertical structure. This study focused on stand attributes of trees
per hectare, basal area per hectare, and average height to diameter
ratio. The objective was to assess sampling alternatives to identify
those that best account for the complexities of riparian areas and
therefore are appropriate to monitoring riparian forest structure.
The riparian areas of interest in this study were associated with
headwater streams. Headwater streams, typically first- or secondorder streams, are different than larger streams (Richardson and
Danehy, 2007) and serve as important habitat for amphibians and
other non-fish vertebrates (Olson and Weaver, 2007). They make up
a high percentage of total stream length (Richardson and Danehy,
2007) and drain much of the overall watershed area (Anderson
et al., 2007). An accurate sampling methodology is important to
characterizing those forest attributes that provide habitat and contribute to species diversity within these stream systems.
Spatial structure is typical for many riparian forest attributes.
Stream to upslope gradients often exist for microclimate (Anderson
et al., 2007), understory vegetation (Pabst and Spies, 1999), and
tree species composition and density (Minore and Weatherly,
314
T. Marquardt et al. / Forest Ecology and Management 260 (2010) 313–320
Fig. 1. Map of DMS site locations (Cissel et al., 2006).
1994). The relative performance of different sampling methods provides information about sources of spatial variation within riparian
zones. Some sampling methods mainly capture variation perpendicular to the stream, while others focus on sampling attributes
parallel to the stream.
In this study we compared the performance of sixteen sampling
methods representing variations of six general design types: simple random sampling (SRS), systematic random sampling (SYRS),
stratified random sampling (STRS), two-stage sampling, horizontal line sampling (HLS) and sector sampling for quantifying trees
per hectare, basal area per hectare, and height to diameter ratio.
The sampling alternatives consisting of different sizes and arrangements of circular plots and rectangular strips were chosen to
address the following hypotheses regarding sources of variation
within riparian areas:
1. Variation is greater moving from the stream to upslope than
moving parallel along the stream.
2. Structural attributes may differ on opposite sides of the stream
such that sampling only one side of the stream will produce
inadequate stand-level estimates.
3. Variation along the length of the streams will be better sampled
with alternating, or staggering strips from one streamside to the
other than a continuous strips that span both sides of the stream.
A variety of methods have been used to compare the quality of
estimates derived from different sampling designs. Common crite-
ria are standard error of the mean (Dahl et al., 2008; Ducey et al.,
2002; Lindsey et al., 1958; Paulo et al., 2005; Schreuder et al., 1987),
and bias (Kenning et al., 2005; Nelson et al., 1998; Schreuder et
al., 1992; Temesgen, 2003; Tokola and Shrestha, 1999). This study
compared the precision and accuracy of stand attributes derived
from each sampling method to the known values determined from
complete census of a stem mapped plot at each of eight headwater
stream locations.
2. Methods
This study was conducted on United States Bureau of Land Management (BLM) Density Management Study (DMS) sites. A primary
goal of the DMS is to evaluate various thinning treatments in young,
relatively uniform stands as means to enhancing structural complexity and the development of older forest characteristics. The
DMS sites are located in the Coast Range and the western foothills
of the Cascade Range in Oregon (Fig. 1). At the time of treatment
between 1997 and 2000 stand ages ranged among sites from 40 to
70 years. Riparian areas associated with headwater streams (generally first- or second-order streams) within experimental density
management treatment units were the focus of this study.
The riparian areas sampled in this study were chosen using a
stratified random sampling scheme. A list of all possible headwater reaches within the DMS was generated from maps and stream
attribute data provided by the US Forest Service. Stream reaches
were stratified to sample two overstory density treatments, three
Table 1
Description of stream reaches sampled from the DMS site locations.
Location
Reach number
BLM district
Density
Buffer
% Slope
Slope class
Aspect
Bottom Line
Keel Mountain
Keel Mountain
Keel Mountain
Keel Mountain
O.M. Hubbard
Ten High
Ten High
13
17
18
19
21
36
46
75
Eugene
Salem
Salem
Salem
Salem
Roseburg
Eugene
Eugene
Moderate
Control
Moderate
Moderate
Moderate
Moderate
Control
Moderate
Two tree height
Control
Two tree height
Two tree height
Variable width
Variable width
Control
Variable width
51
18
21.2
14
38
31
19
33
S
M
M
M
S
S
M
S
NE/SW
N/S
NW/SE
NW/SE
N/S
NW/SE
N/S
N/S
T. Marquardt et al. / Forest Ecology and Management 260 (2010) 313–320
315
Table 2
List of tree parameters measured on each stem mapped tree and the recording
protocol for each measurement.
Tree attribute
Recording protocol
Diameter at breast height
Species
Canopy classification
Nearest 1/10th centimeter
4 Letter code, appendix
Visually determined, 1 letter code,
Dominant (D), Codominant (C),
Intermediate (I), Suppressed (S)
Visually determined, Dead (D), Live (L)
2 Letter code, visually determined
F1-Live, full crown
F2-Partially dead crown
F3-Dead crown
S1-Two or more crowns
S2-One crown broken off
B1 to B5—snags with different size classes
2 Letter code, visually determined
Condition
Crown class
Decay class
Fig. 2. Illustration of plot layout on the sampled stream reach. The centerline of the
72 m square block was oriented in the general direction of the stream. Sampling of
trees took place 36 m from the centerline to upslope.
uncut buffer treatments, and two channel sideslope classes. Of
twelve reaches originally selected for sampling time constraints
limited sampling to eight reaches (Table 1). The two density management treatments were an unthinned control with 200–350 trees
per acres (TPA) (494–865 trees per hectare) and moderate density
retention where 60–65% of the stand had been thinned to 80 TPA
(198 trees per hectare). Buffer treatments consisted of a two site
potential tree height buffer (2SPTH), a variable width buffer and an
unthinned control. The 2SPTH buffer is measured in slope distance
from the stream center and is based on the 50 year site index height
of trees for each site, on average 146 ft (44.5 m). The variable width
buffer had a minimum width of 15.2 m each side of the stream,
but varied based on channel topographic features or the inclusion
of sensitive areas, such as those prone to landslide or where plant
species of concern were present. Reaches were stratified between
those having sideslopes less than 30% or greater than 30%.
One 0.518 ha (72 m × 72 m) square sample plot was randomly
located along each of the headwater streams. The plot ran 72 m
parallel to the stream and 36 m upslope, on each side of a centerline
anchored in the stream channel at the upper and lower ends of
the stem mapped sample plot (Fig. 2). Randomization of sample
plot locations was accomplished by measuring the available length
of stream reach from GIS stream layers and generating a random
number to determine to the nearest location of the downstream
end of the block. On site, a laser rangefinder was used to locate the
predetermined plot location for each stream.
On each 0.518 ha plot the positions of all woody stems greater
than 6.9 m tall or 7.6 cm breast height diameter (dbh) were mapped
using Total Station Survey Equipment. A survey-grade GPS was
used to determine the coordinates for mapping control points (station locations). A reflector was held against the outside of the tree
or within 0.3 m of the center of the tree. The distance to each tree
(estimate of precision for distance) was calculated by internal software based on the bearing from the station to the tree, and the
latitude and longitude of the station. The size of the plot and the
density of stems required mapping from multiple control locations
per plot.
Tree observations including breast height diameter (DBH),
species, condition, canopy classification, crown class, and decay
class were made and recorded during stem mapping (Table 2).
Diameter was measured with a diameter tape to the nearest
0.1 cm at a stem height of 1.37 m on the uphill side of the tree.
Multiple-stemmed trees forking below 1.37 m were counted as
multiple trees. Diameter was measured above any stem abnormalities such as bulging. Pistol butt or leaning trees were measured
at 1.37 m along the stem. The condition of the tree was visually
assessed. A tree without any green foliage was considered dead; a
tree having any green foliage was considered live.
Table 3
Description of the sampling alternatives examined in this study including the number of plots simulated at the 10% and 20% sampling intensity. Under “Shape”, R = rectangular,
C = circular, and T = transect, and Ra = radial plot.
Sampling alternative
Description
Size
Shape
Plots (10%)
Plots (20%)
FAP5R
FAP9R
FAP5S
FAP9S
Random fixed area plots
Random fixed area plots
Systematic fixed area plots
Systematic fixed area plots
5.64 m radius
9 m radius
5.64 m radius
9 m radius
C
C
C
C
5
2
5
2
10
4
10
4
ASTP3
ASTP7
Alternate perpendicular strips
Alternate perpendicular strips
3.6 m × 36 m
7.2 m × 36 m
R
R
4
2
8
4
PEST3
PEST7
Perpendicular strips
Perpendicular strips
3.6 m × 72 m
7.2 m × 72 m
R
R
2
1
4
2
OSSP3
OSSP7
Perpendicular, one side only
Perpendicular, one side only
3.6 m × 36 m
7.2 m × 36 m
R
R
4
2
8
4
PAST3
PAST9
STRS parallel strip sampling
STRS parallel strip sampling
3.6 m × 36 m
9 m × 28.8 m
R
R
4
2
8
4
HLS08
HLS10
Horizontal line sampling
Horizontal line sampling
BAF 8
BAF 10
22 m T
27 m T
2
2
4
4
SEC11
SEC22
Sector sampling
Sector sampling
11.46◦
22.92◦
36 m Ra
36 m Ra
4
2
8
4
316
T. Marquardt et al. / Forest Ecology and Management 260 (2010) 313–320
The sixteen sampling design alternatives (Table 3) were evaluated by simulation using SAS (v. 9.1, SAS Institute, 1990). All
hardwoods and dead conifers were removed from the dataset and
the sampling designs were evaluated for live conifer trees only.
Because the relative abundance of hardwoods and dead trees was
generally small, it was assumed that different sampling designs
better suited to rare or highly variable phenomenon would be
needed to sample these features. Sampling of the hardwood and
snag component is being addressed in a separate study (Marquart
et al., in preparation). To address edge effects associated with the
stem mapped area, the plot data was wrapped edge to end. Each
design was simulated for both a 10% (0.1*722 = 518.4 m2 ) and a 20%
(0.2*722 = 1036.8 m2 ) sampling intensity.
Each of the sixteen sampling alternatives was implemented
in simulation 500 times with a different random starting point
for each simulation. The plot center coordinates were randomly
selected and the number of sample plots per design varied with
plot size and sampling intensity (Table 3).
Simple random sampling (SRS) used circular, fixed area plots
with radii of 5.64 m or 9 m. Systematic random sampling (SYRS)
used circular plots as well as several strip sampling alternatives. The
alternating strip designs (ASTP3 and ASTP7, Table 3) were distinct.
These designs were simulated by breaking the 72 m grid into either
3.6 m or 7.2 m wide strips which were 36 m in length. The strips
were oriented perpendicular to the centerline of the plot (Fig. 2),
approximately perpendicular to the stream. Each strip consisted of
a rectangular plot on one side of the stream and the rectangular
strip diagonal to it on the opposite side of the stream. For example, one could think of this as running a transect perpendicular
to the stream and sampling a 3.6 m strip to the left of the transect line on one side of the stream, and all trees within 3.6 m to
the right of the transect line on the opposite side of the stream.
Stratified random sampling (STRS) was used to sample strips running parallel to the stream, but also with at least one strip close
to the stream, and another upslope. For the 9 m option, the 72 m
grid was first split into 9 m strips running parallel to the stream;
the two outermost strips on either side of the stream comprised
one stratum and the four innermost strips comprised a second
stratum.
Two-stage sampling was simulated as sampling only one side of
the stream using the strip sampling approach. The stream side to
be sampled was selected in the first stage. In the second stage, the
selected sample area was broken into strips that were systematically sampled. This approach was simulated using strips 3.6 m and
7.2 m width, The 500 simulations were evenly distributed between
the two stream sides for each reach.
The horizontal line sampling (HLS) alternative provided designs
using variable radius plots to the comparison. Each transect for the
HLS design began at the centerline of the plot and were placed
perpendicular to the stream. Lynch’s (2006) equations were used
to expand the data from each transect(s) to a per hectare basis. Two
BAF were chosen based on the approximate amount of area that was
sampled. Unlike the other alternatives that ran 36 m perpendicular
to the stream, this alternative sampled at 22 m and 27 m upslope
from the stream for the 8 BAF and 10 BAF alternatives respectively.
The sector sampling design was adapted from Iles and Smith
(2006). For this study, the sector was essentially a fixed area plot
to simplify area calculations. First, a 36 m radius fixed area circular plot was selected randomly within the 72 m grid. Next, two to
four sectors of either 11.46◦ or 22.92◦ were sampled depending on
the alternative. Sectors were sampled based on a bearing that was
randomly generated as a starting point for the first plot. Remaining plots were systematically sampled. In the 20% intensity design
for the 11.46◦ sized sector, two 36 m fixed area plots were placed
within the 72 m grid and four sectors were sampled from each of
the circular plots.
Three methods were used to evaluate each of the sampling
designs compared to the actual stem map. The designs were
evaluated based on how well they predicted trees per hectare
(TPH), basal area per hectare (BAPH) and height to diameter ratio
(H/D) using root mean square error (RMSE), absolute percent bias
(APB), and mean absolute deviation (MAD). Individual tree heights
were estimated using a height-diameter equation based on the
Chapman–Richards function (Richards, 1959) as applied by Garman
et al. (1995) for western Oregon species. Height to diameter ratio
was calculated based on estimated height and measured diameter.
The RMSE was computed as:
500
k=1
RMSE =
2
(Ŷk − Y )
500
(1)
where Ŷk is the estimated attribute (TPA, H/D, or BAPH) for the kth
replication and Y is the known attribute value.
All the selected sampling alternatives are known to be unbiased,
so the traditional measure of bias was not computed. Instead, an
absolute value of the cumulative bias was used. It is the average
of the absolute value of the percent bias for each replication. The
absolute value does not allow one to know if the alternative is over
or underestimating the mean, but only by how much. The equation
used to estimate absolute percent bias is as follows:
APB =
500 Ŷk −Y k=1 Y 500
(2)
where Ŷk is the estimated attribute (TPA, H/D, or BAPH) for the kth
replication and Y is the known attribute value.
MAD was used as a measure of variation from the mean of the
72 m square subpopulations. The equation used to estimate MAD
is as follows:
MAD =
500 Ŷk − Y k=1
500
(3)
where Ŷk is the estimated attribute (TPA, H/D, or BAPH) for the kth
replication and Y is the known attribute value.
3. Results
Estimates of TPH had RMSE values that ranged from 64.3 to 261.8
for 10% sampling intensity and from 40.4 to 261.6 for 20% sampling
intensity (Table 4). ASTP3 and PEST3 had the smallest values. The
RMSE values for BAPH (m2 ) ranged from 8.5 to 28.3 for the 10%
sampling intensity and 5.6 to 28.4 for the 20% sampling intensity.
ASTP3 and ASTP7 had the smallest values. The RMSE values for the
height to diameter ratio ranged from 1.3 to 2.4 for the 10% sampling intensity and from 0.8 to 1.9 for the 20% intensity. ASTP3 and
PEST3 estimated height to diameter ratio most accurately. Standard
deviations suggested that the variation among estimates was quite
large for HLS08, HLS10, and OSSP3 (Table 4).
Absolute percent biases when estimating TPH, BAPH and H/D
ratio were least using ASTP3, ASTP7, PAST3, and PEST3 designs
(Table 5). The standard deviation about the mean was relatively
large for FAP5S and FAP9S. Standard deviations ranged from 15.8%
to 61.4% and 9.7% to 61.3% when estimating TPH at the 10% and
20% intensity respectively. When estimating BAPH, absolute percent bias values ranged from 16.8% to 56.0% for the 10% intensity
and 11.0% to 56.1% for the 20% intensity. The alternatives that performed well when estimating the height to diameter ratio were the
ASTP3, ASTP7, PAST3, PEST3, SEC11, FAP5S and PEST7 alternatives.
Values ranged from 1.7% to 3.0% for the 10% sampling intensity and
from 1.0% to 3.0% for the 20% intensity (Table 5).
Sampling alternatives that performed well when evaluated
using MAD were ASTP3, ASTP7, PAST3, PEST3, PEST7, and SEC11
T. Marquardt et al. / Forest Ecology and Management 260 (2010) 313–320
317
Table 4
Summary of sampling alternatives evaluated using RMSE. Values under trees per hectare (TPH), basal area per hectare (BAPH, m2 ) and height to diameter ratio (H/D) are the
mean RMSE values from the eight locations. Shaded values are the five smallest. “SD” is the standard deviation of the mean RMSE.
Sampling alternative
Intensity
TPH
BAPH (m2 )
H/D Ratio
SDTPH
SD BAPH (m2 )
SDH/D ratio
ASTP3
ASTP7
FAP5R
FAP5S
FAP9R
FAP9S
HLS08
HLS10
OSSP3
OSSP7
PAST3
PAST9
PEST3
PEST7
SEC 11
SEC22
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
64.3
71.0
83.2
105.1
94.3
115.2
261.8
260.0
211.2
91.0
66.6
94.0
64.5
70.3
90.4
90.1
8.5
8.5
10.5
12.6
11.3
13.7
28.3
27.9
25.4
12.0
9.0
11.6
9.1
9.4
11.1
10.5
1.3
1.7
1.7
1.7
1.9
2.3
2.4
2.2
2.3
1.9
1.5
2.0
1.4
1.7
1.7
1.8
11.5
17.0
15.5
29.1
16.6
21.7
80.8
82.7
53.9
45.1
20.6
27.0
11.3
16.5
17.3
12.7
1.9
2.1
1.6
3.5
2.1
2.9
6.5
6.0
5.3
8.5
1.1
2.5
2.3
1.9
1.6
1.9
0.5
0.8
0.5
0.5
0.8
1.1
0.8
0.9
0.8
0.8
0.6
0.8
0.5
0.8
0.8
0.7
ASTP3
ASTP7
FAP5R
FAP5S
FAP9R
FAP9S
HLS08
HLS1O
OSSP3
OSSP7
PAST3
PAST9
PEST3
PEST7
SEC 11
SEC22
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
40.4
41.5
60.2
51.1
87.3
101.9
261.6
260.5
214.0
55.0
45.9
49.7
42.3
46.1
53.2
71.2
5.6
5.6
7.5
6.2
9.4
10.5
28.4
28.0
25.6
6.7
6.1
6.7
6.2
6.0
7.0
8.0
0.8
1.0
1.2
0.9
2.3
2.2
1.9
1.8
1.8
1.5
1.1
1.2
0.9
1.0
1.2
1.3
14.2
7.6
11.1
23.5
22.5
31.3
81.1
82.5
53.9
21.8
14.9
15.7
18.7
9.1
12.9
14.2
1.8
1.5
1.2
1.3
1.9
3.1
6.6
6.0
5.4
2.5
0.9
1.2
2.5
1.5
1.3
1.7
0.3
0.5
0.4
0.2
1.1
1.1
0.9
0.9
0.8
0.9
0.5
0.6
0.4
0.4
0.9
0.8
Table 5
Summary of performance of sampling alternatives evaluated using APB. Values under trees per hectare (TPH, %), basal area per hectare (BAPH, %) and height to diameter ratio
(H/D, %) are the mean APB values from the eight locations. Shaded values are the five smallest percentages. “SD” is the standard deviation of the mean APB for TPH, BAPH,
and H/D.
Sampling alternative
Intensity
TPH
BAPH (m2 )
H/D ratio
SDTPH
SD BAPH (m2 )
SDH/D ratio
ASTP3
ASTP7
FAP5R
FAP5S
FAP9R
FAP9S
HLS08
HLS10
OSSP3
OSSP7
PAST3
PAST9
PEST3
PEST7
SEC 11
SEC22
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
15.9%
17.2%
20.1%
25.6%
22.8%
28.2%
61.4%
60.7%
49.7%
22.1%
16.0%
22.5%
15.8%
17.0%
22.3%
22.2%
16.8%
17.1%
21.0%
25.7%
22.7%
27.6%
56.0%
55.2%
50.1%
22.4%
18.4%
23.3%
17.8%
18.9%
22.7%
21.3%
1.7%
2.2%
2.2%
2.2%
2.5%
3.0%
3.1%
2.9%
3.0%
2.5%
1.9%
2.5%
1.8%
2.2%
2.2%
2.3%
4.6%
4.8%
3.1%
8.2%
3.6%
6.2%
5.8%
5.4%
0.4%
11.6%
4.2%
5.4%
3.8%
4.5%
6.6%
5.8%
2.5%
4.5%
2.7%
8.9%
3.4%
5.2%
6.2%
4.7%
0.5%
11.1%
4.2%
5.8%
3.2%
3.7%
5.6%
4.4%
0.6%
1.1%
0.7%
0.7%
1.1%
1.5%
1.1%
1.1%
1.1%
1.1%
0.7%
1.1%
0.7%
1.1%
1.0%
0.9%
ASTP3
ASTP7
FAP5R
FAP5S
FAP9R
FAP9S
HLS08
HLS1O
OSSP3
OSSP7
PAST3
PAST9
PEST3
PEST7
SEC 11
SEC22
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
9.7%
10.1%
14.5%
11.8%
21.2%
25.0%
61.3%
60.8%
50.4%
13.0%
11.0%
11.9%
9.9%
11.4%
13.3%
17.7%
11.0%
11.0%
15.0%
12.5%
18.6%
21.4%
56.1%
55.3%
50.5%
13.3%
12.5%
13.8%
12.1%
11.7%
14.1%
16.3%
1.0%
1.2%
1.6%
1.2%
3.0%
2.9%
2.4%
2.3%
2.3%
2.0%
1.4%
1.5%
1.2%
1.3%
1.5%
1.7%
2.6%
2.4%
1.9%
3.4%
5.7%
8.3%
5.7%
5.3%
0.3%
3.8%
3.0%
3.7%
3.0%
3.6%
5.3%
5.8%
2.8%
2.4%
2.0%
2.4%
1.6%
7.4%
6.0%
4.6%
0.3%
3.6%
3.1%
3.7%
4.5%
1.3%
3.0%
4.6%
0.4%
0.6%
0.5%
0.3%
1.4%
1.4%
1.1%
1.1%
1.1%
1.2%
0.6%
0.8%
0.6%
0.5%
1.1%
1.0%
318
T. Marquardt et al. / Forest Ecology and Management 260 (2010) 313–320
Table 6
Summary of performance of sampling alternatives evaluated using MAD. Values under trees per hectare (TPH), basal area per hectare (BAPH m2 ) and height to diameter ratio
(H/D) are the MAD values from the eight locations. Shaded values have the smallest MAD. “SD” is the standard deviation of the mean APB for TPH, BAPH, and H/D.
Sampling alternative
Intensity
TPH
BAPH (m2 )
H/D ratio
SDTPH
SD BAPH (m2 )
SDH/D ratio
ASTP3
ASTP7
FAP5R
FAP5S
FAP9R
FAP9S
HLS08
HLS10
OSSP3
OSSP7
PAST3
PAST9
PEST3
PEST7
SEC 11
SEC22
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
64.3
71.0
83.2
105.1
94.3
115.2
261.8
260.0
211.2
91.0
66.6
94.0
64.5
70.3
90.4
90.1
8.5
8.5
10.5
12.6
11.3
13.7
28.3
27.9
25.4
12.0
9.0
11.6
9.1
9.4
11.1
10.5
1.3
1.7
1.7
1.7
1.9
2.3
2.4
2.2
2.3
1.9
1.5
2.0
1.4
1.7
1.7
1.8
11.5
17.0
15.5
29.1
16.6
21.7
80.8
82.7
53.9
45.1
20.6
27.0
11.3
16.5
17.3
12.7
1.9
2.1
1.6
3.5
2.1
2.9
6.5
6.0
5.3
8.5
1.1
2.5
2.3
1.9
1.6
1.9
0.5
0.8
0.5
0.5
0.8
1.1
0.8
0.9
0.8
0.8
0.6
0.8
0.5
0.8
0.8
0.7
ASTP3
ASTP7
FAP5R
FAP5S
FAP9R
FAP9S
HLS08
HLS1O
OSSP3
OSSP7
PAST3
PAST9
PEST3
PEST7
SEC 11
SEC22
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
20%
40.4
41.5
60.2
51.1
87.3
101.9
261.6
260.5
214.0
55.0
45.9
49.7
42.3
46.1
53.2
71.2
5.6
5.6
7.5
6.2
9.4
10.5
28.4
28.0
25.6
6.7
6.1
6.7
6.2
6.0
7.0
8.0
0.8
1.0
1.2
0.9
2.3
2.2
1.9
1.8
1.8
1.5
1.1
1.2
0.9
1.0
1.2
1.3
14.2
7.6
11.1
23.5
22.5
31.3
81.1
82.5
53.9
21.8
14.9
15.7
18.7
9.1
12.9
14.2
1.8
1.5
1.2
1.3
1.9
3.1
6.6
6.0
5.4
2.5
0.9
1.2
2.5
1.5
1.3
1.7
0.3
0.5
0.4
0.2
1.1
1.1
0.9
0.9
0.8
0.9
0.5
0.6
0.4
0.4
0.9
0.8
(Table 6). The values ranged from 64.3 to 261.8 when estimating TPH at the 10% intensity and from 40.4 to 261.6 for the 20%
intensity. Sampling alternatives that did not perform well included
HLS08, HLS10, and FAP9S. When evaluated for their ability to estimate BAPH, values ranged from 8.5 to 28.3 at the 10% intensity
and 5.6 to 28.4 at the 20% intensity. When estimating the height to
diameter ratio, values ranged from 1.3 to 2.3 and from 0.8 to 2.3 at
the 20% intensity. The alternative that performed best overall was
ASTP3.
The sector sampling alternative using 11.46 degree sector
(SEC11) did not appear to perform well overall, but performed well
several times at the different locations. The alternative that most
frequently performed well at the eight locations was ASTP3 alternative. Other alternatives that performed well were SEC11 and ASTP7.
Sampling alternatives that performed well at multiple sites when
estimating BAPH were PEST3 and ASTP3. Several alternatives performed well when estimating TPH. PAST3, ASTP3, ASTP7, and PEST3
all performed well in estimating BAPH, TPH, and H/D ratio at multiple sites. The majority of the sampling alternatives that performed
well at more than one location also performed well when evaluated
using RMSE, APB and MAD. These included ASTP3, ASTP7, PAST3,
PEST3, and PEST7.
4. Discussion
The designs that performed best were generally those that sampled perpendicular to the stream. The best performing designs were
the SYRS designs that used rectangular shaped plots. However, the
STRS designs (PAST3, PAST9) also performed well. The alternatives
that performed poorly in this simulation were OSSP3, FAP9R, FAP9S,
HLS10, and HLS08 alternatives. Overall, ASTP3 performed the best
among the alternatives. However, PEST3, ASTP7, and PAST3 alternatives also performed well.
In this comparison of alternatives, the circular fixed area plots
did not perform as well as the rectangular plots. The smaller 5.64 m
radius plots performed better than the 9 m radius plots. The FAP5S
performed best among the circular fixed area plots at the 20%
intensity, but the FAP5R alternative outperformed the other circular fixed area plots at the 10% intensity. These designs performed
similarly whether evaluated using MAD, APB, or RMSE. The poor
performance of the other designs could be attributed to plots falling
entirely within gaps in the canopy or under-representing conifers
upslope from the stream.
STRS design performed better than all other designs except for
the rectangular SYRS designs. PAST3 performed better than PAST9
overall. The alternative performed similarly in estimating TPH,
BAPH or H/D. Because the rectangular strips of PAST3 and PAST9
were oriented parallel to the stream, one would have expected the
alternatives to perform poorly if there was one prominent gradient within riparian areas that existed from the stream to upslope.
Even though strips were placed using stratified sampling, the performance of these design indicates that in addition to the strong
lateral gradients extending upslope from the stream there are other
sources of longitudinal variation in these riparian areas.
Although ASTP3 performed the best at the most locations and
had the lowest amount of error, PEST3, PEST7 and ASTP7 also performed very well with respect to RMSE, APB, and MAD.
These two-stage designs performed inconsistently throughout
this analysis. The OSSP7 alternative (7.2 m wide strips) performed
well at several locations, but OSSP3 alternative (3.6 m wide strips)
did not perform well at any of the locations. One would expect
that stand attributes would differ markedly for opposing north and
south facing slopes bounding a steeply incised stream. About half
of the locations sampled appeared in the field to have fairly symmetrical selected stand attributes each side of the stream. The poor
performance of OSSP3 shows that when a source of variation within
T. Marquardt et al. / Forest Ecology and Management 260 (2010) 313–320
a riparian area is ignored, sampling designs perform poorly. Overall, this design is not recommended for use in sampling selected
stand attributes.
Even though the HLS alternatives performed well when estimating height to diameter ratio, the rectangular strip designs were
more consistent. Unlike other alternatives, the HLS alternatives did
not sample the full 36 m on either side of the stream. Schreuder et al.
(1987) suggested that using longer lines with a larger angle gauge
will lead to more accurate samples. If one was going to evaluate this
design again, increasing the transect length to 36 m would be recommended. Even though HLS10 had the smallest error at the 20%
intensity, it was not among the best overall performing designs.
Kenning et al. (2005) found that a modified horizontal sampling
design was more efficient in sampling basal area compared to fixed
area sampling. Several research studies have found this design to be
time-efficient and perform well (Kenning et al., 2005; Schreuder et
al., 1987, 1992), especially in forests with larger diameter trees. Had
a longer transect line been used in this study, one would suspect it
would have been able to perform among the top designs.
The modified sector sampling design was suggested for use
when sampling small clusters of objects by Iles and Smith (2006).
In sector sampling an 11.46 wide angle performed better than a
22.92 wide angle. Use of a random azimuth in sector sampling created the potential for only the trees closest to the stream to be
sampled rather than sampling from the stream to upslope. It may
have been better to orient the sectors opposite each other with
the center point in the stream. This alternative did perform well
at several of the locations when evaluated using RMSE, APB, and
MAD. Although sector sampling was not among the worst alternatives, it was generally outperformed by ASTP3, ASTP7, PEST3 and
PEST 7.
Although this study did not specifically focus on plot size, there
were some trends that emerged. The fixed area circular shaped
plots performing the best were 5.6 m radius in size. The larger 9 m
plot size may not have been as efficient in capturing the variation
occurring parallel to the stream. In stratified designs, there were
more 3 m wide strips to choose from and strips landing on or in the
stream may have been sampled less frequently. In general, PEST3
and ASTP3 performed better than ASTP7 and PEST7 alternative. One
would expect the larger strip width to perform better. In a prior
study, Lynch (2003) found that as plot size increased from 0.01 to
0.05 ha, precision increased, but did not increase enough to justify the larger plot size which was consistent with the findings of
Maclean and Ostaff (1983). The OSSP7 alternative performed much
better than OSSP3. Doubling the strip width allows one to capture
more variability at a local (i.e., plot) level, but there are half as many
strips throughout the area if the sampling intensity is maintained
at the same level. Nelson et al. (1998) found that widths of rectangular plots best for measuring forest canopy height were at least
6–8 m in width. It should be noted that there were a limited number of plot sizes evaluated for each of the sampling alternatives and
that the stream size and location likely played a role in the results
of each alternative.
Throughout this study, rectangular plots performed better than
other shapes. When comparing circular fixed area plots to rectangular plots, Johnson and Hixon (1952) found that rectangular plots
outperformed circular plots. ASTP3, ASTP7, PEST3, and PEST7 generally had the smallest difference from the actual mean at each
site. The only exception was the performance of HLS for estimating
height to diameter ratio. Husch et al. (2003, p. 329) note that “it is
desirable to orient strips at right angles to the drainage pattern in
order to increase the likelihood of having the strip intersect all stand
conditions.” The alternatives using circular fixed area plots may
not have done a good job of intersecting the different stand conditions when moving from stream to upslope. Despite the circular
fixed area alternatives performing well in some cases, these alter-
319
natives were much less consistent than the rectangular alternatives
in accurately estimating TPH, BAPH, and H/D.
The source of spatial variation most pivotal to determining the
effectiveness of a sampling design occurred along slopes running
upslope from the stream. It is difficult for a sampling design to provide reliable estimates of TPH, BAPH, or H/D without capturing the
gradients present within riparian areas. In comparing PEST3, PEST7,
PAST3 and PAST9, one can see that PEST3 and PEST7 did better at
estimating TPH, BAPH and H/D. PAST3 alternative did perform well
when estimating TPH, but was inconsistent in estimating BAPH and
H/D at the individual locations. In addition, alternatives that did not
sample both sides of the stream were outperformed by those that
sampled from both sides of the stream. This can be seen in the
performance of OSSP3 and OSSP7 compared to PEST3 and PEST7.
ASTP3 and ASTP7 performed similarly to PEST3 and PEST7. However, PEST3 and ASTP3 performed well at a variety of locations.
Variation running parallel to the stream impacted the performance
of the sampling alternatives and alternating the strips across the
stream led to more accurate estimates. In addition, the smaller strip
widths may have captured the patchiness of the trees within this
location. Overall, ASTP3 alternative performed better than the other
alternatives examined.
Because of the lack of data relating to sampling or measurement costs, none of the sampling alternatives were examined for
cost of plot layout and measurement or sampling time required to
execute them. Further research is warranted to identify the most
cost-efficient design, which will depend on the underlying pattern
of variability and on the issues affecting the time to obtain the measurements (e.g., difficulty of crossing the stream to work on both
sides).
5. Conclusion
From this analysis, one can see that there is a high amount of
variation within riparian areas, even those located relatively close
to each other. Although some alternatives performed quite a lot better than others, the standard deviation around the mean was quite
large for some of the alternatives. Overall, rectangular strip plots
outperformed all other plot shapes. Plot sizes varied from 3.6 m in
width to 9 m in width. In general the narrower strip widths performed better than the wider strip widths. Although the wedge
shaped sector sampling alternative did perform well at some of the
locations, it did not perform among the most accurate alternatives
overall. The circular shaped plots performed better than the alternatives that used horizontal line sampling. In addition, one would
have expected a greater decrease in error as one moved from the
10% to 20% sampling intensity.
This analysis was conducted using small scale stem maps from
eight headwater streams in western Oregon. Under these conditions, ASTP3 alternative was found to be the most accurate and
was able to perform well at the eight locations. This alternative
consisted of rectangular plots systematically sampled. The rectangular plots were offset 3.6 m wide strips each side of the stream. The
other alternatives that performed well were ASTP7, PEST3, PEST7,
and PAST3. The alternatives that did not perform well included the
circular fixed area plots that were 9 m in radius. In general, strips
oriented perpendicular to the stream outperformed those oriented
parallel to the stream.
Acknowledgements
We gratefully acknowledge the cooperation and financial
support provided by the Pacific North West Research Station
(agreement number: 04-JV-11261953-414), Bureau of Land Management and the DMS Site coordinators. We thank Timothy Drake,
320
T. Marquardt et al. / Forest Ecology and Management 260 (2010) 313–320
Andrew Neill for their supporting in the data collection phase, and
Drs. Bianca Eskelson and Kim Iles for their insights and comments
on an early draft.
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